Question

Mark (✓) against the correct answer
If ${\left(\frac{5}{3}\right)}^{-5}\times {\left(\frac{5}{3}\right)}^{11}={\left(\frac{5}{3}\right)}^{8x}$, then x = ?

(a) $\frac{-1}{2}$
(b) $\frac{-3}{4}$
(c) $\frac{3}{4}$
(d) $\frac{4}{3}$

Answer 1

(c) $\frac{3}{4}$

${\left(\frac{5}{3}\right)}^{-5}\times {\left(\frac{5}{3}\right)}^{11}={\left(\frac{5}{3}\right)}^{8x}$
⇒ ${\left(\frac{5}{3}\right)}^{-5+11}={\left(\frac{5}{3}\right)}^{8x}$ [ since $a^m\times a^n=a^{m+n}$]
⇒ ${\left(\frac{5}{3}\right)}^6={\left(\frac{5}{3}\right)}^{8x}$
On equating the coefficients:
6 = 8x
∴ x = $\frac{6}{8}=\frac{3}{4}$